Method and device for generating a random signal and digital-to-analog converting systems using same

ABSTRACT

A process and device for generation of a random signal, and a digital-analog conversion system using such a random signal. The process includes a first noise generation step, a second noise filtering step to obtain a signal x(t) with a predetermined spectral envelope H(f), a third step in which a non-linear function g is applied to the signal x(t) in order to give a signal y(t) similar to a predetermined amplitudes histogram f(y), the function g being defined by the following relation:        y   =       g        (   x   )       =     α          ∫   0   x              P        (   u   )         f        (   u   )                 u                             
     where the function P is the histogram of the signal x(t) to which the third step is applied, and a fourth step in which a pulse response filtering w(t) is applied to the signal y(t) to correct its spectral envelope and obtain an output signal s(t) with a predetermined spectral envelope H(f). The pulse response w(t) is the inverse Fourier transform of a frequency function W obtained by dividing the function H(f) by the modulus Y 2 (f) of the Fourier transform of the signal y(t). Such a process, device, and system may find particular application to a direct digital frequency synthesis, such as in radar or instrumentation applications.

This invention relates to a process and device for generation of arandom signal. The invention is particularly applicable to thedigital-analog conversion field and to the analog-digital conversionfield. Consequently, the invention also relates to a digital-analogconversion system using such a random signal. It is applicableparticularly for direct digital frequency synthesis, for example in thefield of radar techniques or instrumentation.

Conversion devices (either digital-analog or analog-digital) are verywidely used in many systems and their performances are usually acritical point in these systems, for example as illustrated by directdigital synthesis.

Direct digital synthesis is a frequency synthesis technique thatconsists of generating digital values of samples of a signal that is tobe generated and converting these samples into analog signals using adigital-analog converter. Signal synthesizers made using this techniqueare very attractive in terms of volume, weight and energy consumption,since they can benefit from large scale integration. Their otheradvantages are particularly excellent resolution and very low switchingtimes from one frequency to another. However, when a useful signal ispassed through the digital-analog converter, it is accompanied by thecreation of parasite signals due to non-linearities of these converters.These non-linearities are due to the fact that not all steps in thedigital-analog converter transfer function are the same height and thatthe transition between steps produces irregular phenomena.

The same problem occurs in applications based on analog-digitalconverters in which the passage of signals in these converters isaccompanied by the creation of parasite signals due to non-linearities.

It is known that adding a random signal to the useful signal beforepassing it through the converter is a means of reducing the level ofparasite signals by reducing the effects of converter non-linearitiesmentioned above. This random signal is frequently called <<dither>>. Theuseful signal usually has a limited band width and the clock frequencyof the system, for example a digital synthesizer, is usually greaterthan this band. This leaves an empty spectral space in which the randomsignal can be placed.

In order to be fully efficient, this random signal must have somespecific characteristics. Firstly, its spectrum must be controlled sothat it does not encroach the useful signals band. Secondly, the qualityof the converter linearization depends on the histogram of timeamplitudes of the random signal. For example, the linearization achievedusing a Gaussian law is not as good as can be obtained with arectangular law. Therefore, there is a real advantage in being able tocontrol the spectrum and the histogram at the same time, for the randomsignal.

Methods are known for obtaining a random signal with a given spectralenvelope. Methods are also known for obtaining a random signal with agiven amplitude distribution law. In particular, these methods aredescribed in books describing probability calculations, for example suchas the book entitled: <<Simulation déterministe du hasard>>((<<Deterministic simulation of chance>> by J. Maurin, published byMasson. However, there is no known method of creating a random signalwhen the spectral envelope and the amplitude distribution law areimposed simultaneously.

In particular, the purpose of the invention is to enable theconstruction of a random signal when the previous two parameters areimposed on it, in other words:

the spectral envelope of the signal, which is actually the modulus ofthe Fourier transform of its correlation function;

the time amplitude distributions law that will subsequently be calledthe amplitudes histogram.

Consequently, the purpose of the invention is a process for thegeneration of a random signal, characterized in that it comprises atleast:

a first noise generation step;

a second noise filtering step to obtain a signal x(t) with apredetermined spectral envelope H(f);

a third step, in which a non-linear function g is applied to the signalx(t) in order to give a signal y(t) similar to a predeterminedamplitudes histogram f(y), the function g being defined by the followingrelation:$y = {{g(x)} = {\alpha {\int_{0}^{x}{\frac{P(u)}{f(u)}{u}}}}}$

where the function P is a histogram of the signal x(t) to which thethird step is applied and α is an amplitude adjustment factor thatdepends on the required amplitude for the signal y(t);

a fourth step in which a pulse response filter w(t) is applied to thesignal y(t) to correct its spectral envelope and obtain an output signals(t) with a predetermined spectral envelope H(f), the pulse responsew(t) being the inverse Fourier transform of a frequency function Wobtained by dividing the function H(f) by the modulus Y₂(f) of theFourier transform of the signal y(t), and then multiplying by a constantβ.

Another purpose of the invention is a device for making use of theabove-mentioned process and a digital-analog conversion system using arandom signal generated according to this process.

The main advantages of the invention are that it improves the linearityof analog-digital and digital-analog converters, that it can be appliedto many systems, and is economic and easy to use.

Other characteristics and advantages of the invention will becomeobvious by reading the following description, made with reference to theattached drawings that represent:

FIG. 1, an illustration of the main possible steps in the processaccording to the invention;

FIG. 2a, an illustration of a third possible step in the processaccording to the invention;

FIG. 2b, an output histogram produced in the second step of the processaccording to the invention;

FIG. 2d, an output histogram produced in the fourth step of the processaccording to the invention, after application of a non-linear functionand filtering;

FIG. 2f, a histogram output from the previous fourth step afterreinjecting the output signal from this step to the input of the thirdstep;

FIGS. 2c and 2 e, illustrations of the above mentioned non-linearfunction as a function of the above mentioned histograms;

FIG. 3, an illustration of a fourth possible step in the processaccording to the invention;

FIG. 4, a sequence of possible steps in the process according to theinvention, repeating the above-mentioned third and fourth steps;

FIG. 5, a possible embodiment of a digital-analog conversion systemusing a random signal generated according to the invention;

FIG. 6a, an example histogram of amplitudes of a generated randomsignal;

FIG. 6b, an example of a useful signal with an amplitude similar to theabove-mentioned random signal;

FIG. 7, a possible embodiment of a digital-analog conversion systemusing a random signal generated according to the invention, alsodeleting truncation errors in the useful signals band;

FIG. 8, a variant embodiment of the system according to FIG. 7;

FIG. 9, an example of an analog-digital conversion system using a randomsignal generated according to the invention.

FIG. 10, an example embodiment of a device for the use of a processaccording to the invention.

FIG. 1 illustrates the possible steps in a process according to theinvention. This process is composed in particular of a sequence of stepsor signal processing operations, including possible repetition of someof the operations in order to make the parameters of the random signalconverge towards the desired laws. These parameters are the parametersmentioned above, in other words the spectrum and the amplitudeshistogram.

The process according to the invention comprises a first step 1 in whicha noise b(t) is generated. For example, this could be white noise, inother words noise with a white spectrum, and with a histogram ofequiprobable amplitudes. For example, this noise b(t) may be produced bya pseudo-random generator like that described in the article entitled<<Generation of pseudo-random sequences for spread spectrum systems>> byR. Moser and J. Stover published in Microwave Journal May 1995. Thenoise generated in the first step is not necessarily white, and may forexample be colored noise. The advantage of white noise is that it isrelatively simple to generate.

In a second step 2 of the process according to the invention, noise b(t)is filtered in order to obtain a signal x(t) with the given spectralenvelope, this spectral envelope being defined by the function H(f),where f is the frequency. For example, this may be obtained by passingthe noise b(t) in a filter which uses the function h(t) equal to theinverse Fourier transform of the previously defined function H(f), asthe pulse response. Therefore the signal x(t) obtained at the outputfrom this second step 2 also has the right spectral envelope but itsamplitudes histogram is close to a Gaussian law. However, this law isnot wanted, in particular because it prevents the generated randomsignal from efficiently eliminating the effect of converternon-linearities, as was mentioned before. A rectangular or almostrectangular law is more efficient in this respect.

For example, if the noise b(t) is not white, the response of the filterin step 2 must be modified accordingly. The role of the filter remainsthe same, particularly to obtain a spectral envelope equal to H(f) atthe output from step 2.

In the third step 3 of the process according to the invention, thesignal x(t) created in the previous step enters into a non-linearelement described by its non-linear transfer function y=g(x). Therefore,a signal y(t)=g[x(t)] is obtained at the output from this third step 3.The non-linear function g is not arbitrary, it is defined such that thesignal y(t) is close to the required amplitudes histogram, thishistogram being defined by a function of y, denoted f(y). For example,this histogram will subsequently be considered as being rectangular, oralmost rectangular.

FIG. 2a illustrates the expression of the function g of the third step.This function g is defined firstly from the histogram 21 of x(t), thefunction of which is denoted P(x), and secondly the required histogram22 for y(t), namely f(y). The function g is then defined according tothe following relation: $\begin{matrix}{y = {{g(x)} = {\alpha {\int_{0}^{x}{\frac{P(u)}{f(u)}{u}}}}}} & (1)\end{matrix}$

α is a factor for adjustment of the amplitude depending on the requiredamplitude for the signal y(t).

This relation (1) shows that the function g that is applied to x(t)actually depends on this variable x(t) since it depends on its histogramP.

For example, the histogram P(x) is obtained as follows:

intervals with equal widths are defined on the scale of amplitudes ofx(t);

a box in the histogram is associated with each interval;

the population of a box is increased by one unit every time that theamplitude of x(t) is included in the interval corresponding to this box.

FIG. 2b illustrates one possible shape of the histogram P(x) of thefunction x(t), at the output from the second step. This histogram isshown by vertical lines 29 each associated with one box 28 of thehistogram. The amplitude of a line corresponds to the population in abox. The ordinates line represents the values of the histogram P(x) as afunction of the amplitudes A of the function x(t) represented on theabscissas line. The histogram P(x) has an approximately Gaussian shape,for example centered on a value x₀ of the function x(t).

FIG. 2c represents a curve 27 showing one possible shape of thenon-linear function g, the centerline of the ordinates representing thevalues g(x) of the function and the centerline of the abscissasrepresenting the values of the amplitudes of x(t). The function g isapproximately linear close to the above mentioned central value x₀.Therefore, these values are hardly affected by the function g, exceptpossibly by a factor. On the other hand, values further away aretransformed by a larger amount, in particular to make the histogram P(x)closer to a square shape. FIG. 2d thus illustrates the role of thenon-linear function g. This figure illustrates the shape of the signalhistogram after the fourth step 4, clearly showing that this histogramis close to a square shape. We will return to this FIG. 2d later whenconsidering the output signal from the next step, and possible loopbacksto the third step 3 and the fourth step 4.

For example, application of function g may be followed and/or precededby a smoothing function 23. This smoothing function may in particular beused to eliminate small insignificant ripples, for example small ripples30 like those in the histogram P(x) illustrated in FIG. 2b. For example,smoothing may be done by a Fourier transform, then by suitable weightingand finally by an inverse Fourier transform. Note that the integralcontained in function g as defined by relation (1) performs smoothing,or almost performs smoothing. If this smoothing is sufficient, it maynot be necessary to perform additional smoothing.

The signal y(t) at the output from the third step 3 actually has therequired histogram f(y), but no longer has the required spectralenvelope H(f) since the consequence of passing through the non-linearfunction was to enrich the spectrum. The spectrum of y(t) then occupiesa wider frequency band than the spectrum defined by the function H(f),and also introduces deformations from this function H(f).

A fourth step 4 of the process according to the invention is used tocorrect the spectral envelope of y(t). This signal y(t) passes through apulse response filter w(t) for this purpose.

FIG. 3 illustrates a method of obtaining this filter w(t) starting fromy(t) and H(f), that is the spectral envelope 34 to be obtained. TheFourier transform of y(t) is calculated by calculation means 31 thatproduce a frequency function f, Y(2πjf) at the output. Means 32 are usedto calculate the modulus of this Fourier transform and thus obtain themodulus |Y(2πjf)|, denoted Y₂(f). For example, these same means may beused to calculate a smoothing to be applied to this function |Y(2πjf)|.As in the third step 3, smoothing may be used to eliminate smallinsignificant ripples. Calculation means 33 subsequently divide H(f) byY₂(f), to give H(f)/Y₂(f). For example, the result of this division maybe multiplied by a factor β that can give the right required timevalues. In particular, this factor β may be used to define the amplitudeof the output signal s(t) mentioned later. For example, thismultiplication may be done for this purpose in the time domain afterapplication of an inverse Fourier transform. The result of the divisionH(f)/Y₂(f) is a function W(f), for which the inverse Fourier transformis determined by calculation means 35, the result of this inverseFourier transform being the function w(t) that is the required pulseresponse. This pulse response that is combined with the filter inputsignal y(t) by a convolution product depends on this input signal y(t).Note that the multiplication by the factor β may be done for exampleafter the division by calculation means 33.

Therefore in the fourth step 4 of the process according to theinvention, the signal y(t) output from the third step passes into apulse response filter w(t), that produces a result s(t) that has therequired spectral envelope and an amplitudes histogram that tendstowards the required function f. It is then possible to repeat step 3 soas to obtain the best approximation of the histogram, and actually torefine the convergence towards the histogram f. FIG. 4 illustrates anexample in which the third step is performed three times and the fourthstep is repeated twice. Thus, at the output from the fourth step 4 thatincludes a pulse response filter w(t), the signal s(t) is once againpassed through the third step 3 a with a non-linear transfer function g2different from the previous function g. This non-linear function g2 isillustrated by curve 27′ in FIG. 2e. This function is defined fromhistogram P(x) illustrated in FIG. 2d, which is the histogram of theoutput signal s(t) from the fourth step, and also the input signal forthe repeated third step 3 a. Since this histogram is closer to a squarethan the previous histogram as illustrated in FIG. 2b, function g2 iscloser to a linear function compared with the previous non-linearfunction, illustrated in FIG. 2c. The histogram of the output signalfrom the repeated fourth step 4 a is illustrated in FIG. 2f. This figureshows a histogram P(x) that is approximately a square or a rectangle.This signal may then be considered as being acceptable for a givenapplication.

Possibly, and if necessary, the signal can then be processed again bythe third step 3 b. The non-linear function g and filtering w(t) aredifferent in each repetition since the non-linearity of the non-linearfunction decreases and the correction to the spectral envelope becomessmaller due to the fact that the spectral envelope and the amplitudeshistogram converge towards the required laws as the repetitions arecontinued. In particular, the number of repetitions of the third andfourth steps depend on the precision with which it is desired toapproach the histogram and the spectral envelope. A histogram shape likethat illustrated in FIG. 2f can thus be quite acceptable.

For example, the repetition may be done by looping the output signals(t) from the fourth step back to the input of the third step asillustrated in loop 5 in FIG. 1. A new non-linear function g, and a newpulse response w(t), are recalculated in each increment in the loop. Thenumber of repetitions of the loop may be defined according to differentcriteria, for example:

the number of repetitions is counted, and the signal s(t) is consideredas being final and repetitions are stopped when the number ofrepetitions reaches a given number;

a convergence criterion may also be used, for example being based on thedifference between the resulting laws and the required laws.

FIG. 5 illustrates application of the process according to the inventionto a digital-analog conversion system, for example contained in adigital synthesizer. In this application, a digital useful signal x(t)must be converted into an analog magnitude with the best possiblelinearity, in other words with as few parasite signals as possible.Therefore, this useful signal x(t) is added to a random signal s(t)obtained by the process according to the invention using generationmeans 54, for example like those described below. The two signals x(t)and s(t) are combined by an adder 51. These two signals are digital. Inone preferred embodiment of the conversion system, the random systems(t) has the following characteristics:

an amplitude similar to or greater than the signal amplitude x(t);

a histogram similar to the equiprobable law with an almost rectangularshape, preferably with edges following laws with continuous derivatives;

a spectral envelope with limited bandwidth, for example this envelopebeing rectangular.

FIGS. 6a and 6 b illustrate the first two of these characteristics. FIG.6a shows a first curve 61 in which the ordinate represents theprobability P that the noise amplitude is included within a giveninterval [A, A+dA]. Consequently, the ordinate represents theprobability P and the abscissa represents the noise amplitude. The noiseamplitude is between a value A_(min) and a value A_(max) defining aninterval [A_(min), A_(max)]. These values are approximately equal to orclose to the minimum and maximum amplitudes of a useful signal, alsorepresented by a curve 62 shown in FIG. 6b, varying between the valuesA_(min) and A_(max). The probability P of the noise is approximatelyconstant over the interval between the values A_(min) and A_(max).Therefore the noise probability density is approximately equal to anequiprobable density law. Note that the useful signal is represented asbeing sinusoidal in FIG. 6b, but obviously other useful signal shapeswould be possible.

The result of the addition x(t)+s(t) by the adder 51 is supported by anN bit bus, the useful signal x(t) and the random signal s(t) being codedon (N−1) bits. Truncation means 52 reduce this result from N bits to Mbits, where M is less than N. The result coded on M bits is convertedinto an analog magnitude by a digital-analog converter 53. If there isno random signal, the transfer of the useful signal through converter 53creates parasite signals particularly due to the non-linearities of theconverter. Non-linearities denote the fact that not all steps in thedigital-analog converter transfer function are the same height, and thetransition between steps produces irregular phenomena. Thesenon-linearities result in the generation of harmonic signals that arealso folded due to sampling. Parasite signals are thus created, aparasite signal being composed of frequencies different from thefrequencies making up the useful signal. In particular, thecharacteristics of the random signal s(t) prevent the energycorresponding to the non-linearity from being organized in discreterays. Consequently, the non-linearity energy is spread into a noisefloor.

The truncation operation also generates parasite signals folded bysampling. Since parasite signals due to non-linearities are reduced to anoise floor, it may also be necessary to solve the truncation problem.FIG. 7 is a mimic diagram showing an embodiment of a digital-analogconversion system in which a sigma-delta modulator is used to eliminatethe truncation error due to converting the useful signal x(t) from Nbits to M bits. For example, truncation is done at the output from theadder 51 that summates the useful signal x(t) and the random signals(t), these two signals each being coded on (N−1) bits. Obviously, ifthere are any non-linearities, there is no point in attempting toeliminate truncation errors, since the parasite truncation signalsremain imperceptible in the other parasite signals, particularly signalscaused by non-linearities. But, as soon as injection of a random signals(t) as described above can eliminate the non-linearities, it becomesadvantageous to add a sigma-delta modulator as described below into adevice according to the invention, in order to eliminate parasitetruncation signals.

The system still comprises means 54 for generating the random signal anda digital-analog converter 53 at the output. The means of generatingrandom signals 54 use the process according to the invention, forexample as described below. Defects due to non-linearities of theanalog-digital converter 53 are processed by these generation means 54.The result of adding the useful signal x(t) and the random signal s(t)is coded on N bits, and for example the amplitude of the signalx(t)+s(t) is chosen to avoid overflows during an addition 73 that willbe described later. The N-bit bus at the output from the adder 51 isdivided into two parts. A first bus comprising the M high order bits isinput into a delay module 71. A second bus comprising the N−M low orderbits is input into the sigma-delta modulator 72. The delay module 51compensates for the delay introduced by the sigma-delta modulator fortreatment of the N−M low order bits. The output from the sigma-deltamodulator 72 is added to the output from the delay module 71 by a secondadder 73. The result of the addition coded on M bits is converted intoan analog signal by the digital-analog converter 53. In particular, thesignal is coded on M bits.

FIG. 8 shows another possible embodiment of the digital-analogconversion system. Two sigma-delta modulators are used in thisembodiment. The first 72 solves the truncation problem for the usefulsignal x(t). The second solves the truncation problem for the randomsystem s(t). This arrangement is advantageous in that in many cases thesecond modulator 82 can either be eliminated since the effect oftruncation of the random signal can be neglected, or integrated into theprocess for generation of the random signal s(t). The result is a savingof equipment. In many cases, truncation of the random signal may beneglected since the spectrum associated with this truncation is verymuch lower than the spectrum related to truncation of the useful signal.This is due to the fact that the energies of the random signal and theuseful signal are similar. In the case of the random signal, this energyis distributed on a large number of spectral components, therefore eachof which is at a level very much lower than the spectral componentrelated to the useful signal. Therefore if these two signals have thesame energy, the amplitude of the rays in the random signal is muchlower than the amplitude of the rays in the useful signal. Thetruncation of the random signal can then be neglected.

Therefore, in this embodiment shown in FIG. 8, the two sigma-deltamodulators 72, 82 are used to independently eliminate truncation errorson the useful signal x(t) and truncation errors on the random signals(t) before these two signals are added, the useful signal and the noisesignal being truncated before this addition. Since the useful signal wascoded on N bits, its bus is divided into two parts. A first buscomprising the M high order bits is input into the first delay module71. A second bus comprising the N−M low order bits is input into thefirst sigma-delta modulator 72. The delay module 71 compensates thedelay introduced by the sigma-delta modulator for processing of the N−Mlow order bits. The output from the sigma-delta modulator 72 is added tothe output from the delay module 71 by a first adder 73. Similarly, thesignal output by random signal generation means 54 is coded on N bits,consequently the output bus from these means is divided into two parts.A first bus comprising the M high order bits of the noise signal isinput into a second delay module 81. A second bus comprising the N−M loworder bits of the useful signal is input into the second sigma-deltamodulator 82. The delay module 81 compensates the delay introduced bythe sigma-delta modulator for processing of the N−M low order bits. Theoutput from the second sigma-delta modulator 82 is added to the outputof the second delay module 81 by a second adder 83. The result of theadditions at the output from the first and second adders 73, 83, codedon M bits, is added by a third adder 84. The result of the additionsupplied by the third adder and coded for example on M+1 bits isconverted into an analog signal by the digital-analog converter 53. Inthis arrangement, the amplitude of the useful signal and of the noisesignal have to be chosen such that the additions 73, 83 do not generateoverflows. As already mentioned, one advantage of the embodimentaccording to FIG. 8 is particularly due to the fact that it enables asaving in terms of equipment if the random signal is generated bycalculation and for example is saved in a read only memory. Inparticular, this can save equipment necessary for the second sigma-deltamodulator 82, the delay module 81 and the adder 83, since the action ofthis assembly is integrated in the calculation means.

In the embodiments of a conversion system according to FIGS. 5, 7 or 8,the analog signal is filtered by a filter (not shown) at the output fromthe digital-analog converter, in order to eliminate the part due to therandom signal, from the converted signal. This filtering of the randomsignal is particularly easy if the signal is perfectly located and doesnot encroach on the useful signals band.

FIG. 9 presents an example application of a process according to theinvention for an analog-digital conversion system. In this case, theuseful signal x(t) and the random signal s(t) are analog signals. Thesetwo signals are added by an analog adder 91. The sum signal x(t)+s(t) ispresent at the input to an analog-digital converter 92, the output ofwhich may for example be coded on N bits. The random signal may forexample have the same characteristics as the signal described in FIG. 6.

Several solutions may be envisaged concerning a device for embodiment ofthe process according to the invention. A computer simulation may beused to calculate the remaining transformations to be applied to a noiseb(t), for example a white noise, to obtain the required random signals(t). This computer actually executes the various steps 1, 2, 3, 4 inthe process according to the invention, possibly repeating the thirdstep 3 and the fourth step 4 one or several times to obtain a sequenceof samples according to a predetermined spectral envelope H(f) and apredetermined histogram f. For example, this sequence of samples may beimplanted in a memory that may be read cyclically or otherwise, forexample by a microprocessor. The addresses of samples in memory are thenused to read the value of these samples and generate the random signal.If several random signals are envisaged, the memory may for examplecontain several different sequences of samples.

FIG. 10 shows a block diagram illustrating another possible exampleembodiment for implementation of the process according to the invention.It comprises means 101 for generating noise, for example equiprobablewhite noise b(t). For example, these means may be composed of apseudo-random generator. The output from these means 101 is connected tothe input of a filter 102 that has a pulse response given by a functionh(t) equal to the Fourier transform of the function H(f) that is thespectral envelope to be obtained. The noise b(t) is thus filtered bythis filter 102. The output from this filter is connected to the inputof a non-linear element 103. In particular, this element comprisescalculation means that apply the relation (1) to the signal x at itsinput in order to obtain the signal y defined by this relation andillustrated in FIG. 2. For example, these calculation means are based onsignal processing processors. For example, the non-linear element 103comprises a memory containing the histogram f(y) to be obtained and oneor several factors α that depend on the signal y(t) to be obtained.Finally, it comprises means of creating the histogram P(x) from theinput signal x(t). For example, these means may be based on amicroprocessor and RAM that may or may not be integrated into theprocessor. The output from the non-linear element 103 is connected tothe input of a second filter 104 with a pulse response w(t) as definedwith reference to FIG. 3. This filter comprises calculation means thatmake the Fourier transform 32 of the signal y(t) at its input and thencalculate the modulus and for example do the smoothing and normalizationof the spectral signal obtained to output the signal Y₂(f). The filtercalculation means 104 also divide H(f) by Y₂(f), where H(f) is thespectral envelope to be obtained for the random signal. For example,this is achieved by the filter 104 comprising a memory that containsthis envelope, thus for example the factor β to define the amplitude ofthe output signal s(t). The filter 104 also comprises means of creatingthe inverse Fourier transform that are applied to the result of thedivision H(f)/Y₂(f) to give the pulse signal w(t), when multiplied by afactor β. The output signal s(t) from the second filter 104 representsthe random signal. However, as already explained, iterations in thethird and fourth steps of the process according to the invention may benecessary to obtain a random signal that satisfies the fixed criteriaconcerning the spectral envelope of this signal and the histogram of itsamplitudes. Consequently, the output from the second filter 104 isconnected to the input of means 105 for validation of the random signalgenerated by the device according to the invention. Validation criteriaare memorized for this purpose in means 105. As long as the signal s(t)at the output from the second filter 104 does not satisfy thesecriteria, the validation means 105 reroute the signal s(t) as an inputto the non-linear element 103. Consequently, an output from validationmeans 105 is connected to the input of the non-linear element. When thesignal s(t) satisfies the validation criteria, it is transferred to asecond output from the validation means 105, this output producing therandom signal. Several criteria may be envisaged, as was describedpreviously.

If a selected criterion is the number of repetitions of signalprocessing through the non-linear element 103 and the second filter 104,the validation means 105 may for example include a counter thatdetermines the number of times that the signal s(t) has been sent to thenon-linear element 103. When the counter indicates the determined numberof iterations, the validation means 105 switch the signal s(t) to theirsecond output. For example, switching may be done using digitalswitches, through or not through a microprocessor.

If a convergence criterion is selected, the validation means 105 may forexample include a digital or analog comparator that compares thehistogram and the spectrum of the signal s(t) with histograms andspectra of memorized reference signals s₀(t). When the result of thiscomparison is within a predetermined and memorized range that satisfiesthe convergence criterion, the validation means 105 switch the signals(t) to the second output to output the random signal.

The device according to the invention as described with respect to FIG.10 may for example be used as a means of generating a random signal 54in the digital-analog conversion systems with relation to FIGS. 5, 7 and8. In the case of an analog-digital conversion system and for FIG. 9, adigital-analog converter may be added at the output from the device,more precisely at the output from the validation means 105 to output ananalog random signal.

When creating an analog random signal, the different steps may also beperformed by analog means. In particular, functions to be performed arecalculated in advance by simulation means and are then performed byanalog circuits based particularly on capacitors, inductances,operational amplifiers and diodes, in a conventional manner. If steps 3and 4 need to be repeated several times, the functions are calculated inadvance for each of the steps to be performed, for example for each ofsteps 1, 2, 3, 4, 3 a, 4 a as illustrated in FIG. 4. Each precalculatedfunction is then executed by analog circuits in which a signal is passedin sequence.

The applications of the invention described above relate todigital-analog or analog-digital conversion applications. Nevertheless,the invention may be applied for many other applications that use arandom signal for which the spectral envelope and the amplitudeshistogram are to be fixed at the same time. Furthermore, the inventionis economic and easy to implement. For a given application, for examplea digital synthesizer, it requires no or few additional components tothe extent that all functions of the invention may be performed bycircuits already used for the application, such as standard processorsor signal processing processors, memories or interfaces. The embodimentmay then be essentially software.

What is claimed is:
 1. Process for the generation of a random signal,comprising: a first noise generation step; a second noise filtering stepto obtain a signal x(t) with a predetermined spectral envelope H(f); athird step in which a non-linear function g is applied to the signalx(t) in order to give a signal y(t) similar to a predeterminedamplitudes histogram f(y), the function g being defined by the followingrelation:$y = {{g(x)} = {\alpha {\int_{0}^{x}{\frac{P(u)}{f(u)}{u}}}}}$

where the function P is the histogram of the signal x(t) to which thethird step is applied and α is an amplitude adjustment factor thatdepends on the required amplitude for the signal y(t); a fourth step inwhich a pulse response filter w(t) is applied to the signal y(t) tocorrect its spectral envelope and obtain an output signal s(t) with apredetermined spectral envelope H(f), the pulse response w(t) being aninverse Fourier transform of a frequency function W obtained by dividingthe function H(f) by the modulus Y₂(f) of the Fourier transform of thesignal y(t), and then multiplying by a constant β.
 2. Process accordingto claim 1, wherein the third and fourth steps are applied to the outputsignal s(t) several times to refine convergence towards thepredetermined histogram and spectral envelope.
 3. Process according toclaim 1, wherein the predetermined histogram is rectangular and thespectral envelope has a limited band.
 4. Process according to claim 1,wherein the predetermined histogram is almost rectangular and thespectral envelope has a limited band.
 5. Process according to claim 4,wherein edges of the histogram have continuous derivatives.
 6. Processaccording to claim 1, wherein the noise in the first step is whitenoise.
 7. Process according to claim 1, wherein in the third step,application of the function g is at least one of followed and precededby a smoothing function.
 8. Process according to claim 1, wherein in thefourth step, the module Y₂(f) is normalized.
 9. Process according toclaim 1, wherein smoothing is applied to module Y₂(f) in the fourthstep.
 10. Device for an embodiment of the process according to claim 1,further comprising at least one computer and a memory, the computerexecuting the steps in the process by simulation to define a sequence ofsamples with a predetermined spectral envelope H(f) and histogram f, thesamples being stored in the memory.
 11. Device for an embodiment of theprocess according to claim 1, further comprising: noise generationmeans; a filter connected to the output of the noise generation means,with a pulse response defined by the function h(t) equal to the Fouriertransform of the function H(f) that is the spectral envelope to beobtained; a non-linear element connected to the filter output,comprising calculation means for applying the function g defined asfollows to the signal x(t) present at its input:$y = {{g(x)} = {\alpha {\int_{0}^{x}{\frac{P(u)}{f(u)}{u}}}}}$

the non-linear element storing a predetermined histogram f(x) and thefactor α in memory, and comprising means for calculating the histogramP(x) of the signal x(t) present at its input; a second filter, connectedto the output from the non-linear element with a pulse response w(t),the second filter comprising calculation means that make the Fouriertransform of the signal y(t) present at its input and then calculate themodulus of the spectral signal obtained to output the signal Y₂(f), thefilter calculation means also dividing H(f) by Y₂(t), the devicecomprising means of memorizing H(f) and a factor β, the filter alsocomprising inverse Fourier transform means that are applied to theresult of the division H(f)/Y₂(f) that can be multiplied by the factor βto give the pulse signal w(t), the output signal s(t) from the secondfilter being the random signal.
 12. Device according to claim 11,wherein the output from the second filter comprises means of validatingthe random signal s(t), validation criteria being memorized in thesemeans, and in that the validation means transfer the signal s(t) to theinput to the non-linear element through an output connected to the inputof this non-linear element, until the signal s(t) at the output from thesecond filter satisfies the validation criteria.
 13. Device according toclaim 12, wherein if a number of repetitions of signal processingthrough the non-linear element and the second filter is selected as acriterion, the validation means comprise a counter that determines anumber of times that the signal s(t) is rerouted to the non-linearelement.
 14. Device according to claim 12, wherein if a convergencecriterion is selected, the validation means comprise a comparator thatcompares the histogram and the signal spectrum s(t) with respect to amemorized histogram and a reference spectrum s₀(t).
 15. Digital-analogconversion system using a random signal s(t) generated by the processaccording to claim 1, wherein a useful digital signal coded on (N−1)bits, may be converted into an analog signal, and comprises: an adder,adding the random signal s(t) coded on (N−1) bits to the useful signal,the result of the addition coded on N bits being truncated to M bits.16. System according to claim 15, further comprising: at the output fromthe first adder, a first bus comprising the M high order bits input intoa delay module; at the output from the first adder, a second buscomprising the N−M low order bits input into a sigma-delta modulator,the delay module compensating for the delay introduced by thesigma-delta modulator for the treatment of N−M low order bits, theoutput from the sigma-delta modulator being added to the output of thedelay module by a second adder, the result of the addition coded on Mbits being converted into an analog signal by a digital-analogconverter.
 17. Digital-analog conversion system using a random signals(t) generated by the process according to claim 1, wherein a usefuldigital signal is to be converted into an analog signal, the usefulsignal and the random signal are coded on N bits being truncated to Mbits, and it comprises two sigma-delta modulators, the useful signal busbeing divided into two parts: a first bus comprising the M high orderbits input into a first delay module; a second bus comprising the N−Mlow order bits input into the first sigma-delta modulator, the delaymodule compensating for the delay input by the sigma-delta modulator forthe processing of N−M low order bits, the output from the sigma-deltamodulator being added to the output of the delay module by a firstadder; a first bus comprising the M high order bits of the random signals(t) input into a second delay module, the bus of this signal beingdivided into two parts; a second bus comprising the N−M low order bitsof the useful signal input into the second sigma-delta modulator, thesecond delay module compensating for the delay input by the sigma-deltamodulator for processing of the N−M low order bits, the output from thesecond sigma-delta modulator being added to the output from the seconddelay module by a second adder; the results of the additions at theoutput from the first and second adders being added by a third adder,the result of the addition produced by this adder coded on M+1 bitsbeing converted into an analog signal by a digital-analog converter. 18.System according to claim 15, wherein it forms a digital synthesizer.